The task of upgrading Malaysia's ageing fleet of fighter jets is being complicated by defence budget cuts, as Prime Minister Najib Razak grapples with growing public discontent over the rising cost of living.
French arms maker Dassault Aviation SA, which builds the Rafale fighter jet, is seen as a frontrunner to supply up to 18 new aircraft to Malaysia's air force in a deal that could be worth more than $2 billion.
The bodies of the two jet pilots - Major Hasri Zahari and Major Yazmi Mohamed Yusof - were found with their parachutes unfurled in a swamp in the state of Terengganu, said Affendi Buang, the chief of the Royal Malaysian Air Force (RMAF).
"We saw the bodies and their parachutes, which means they had ejected from the plane," Affendi told a news conference broadcast on Facebook by Malaysian publication BH Online.
"We have yet to find the plane," he said at the event in Kuantan, about 400 km (249 miles) from Kuala Lumpur, the Malaysian capital.
Authorities lost contact with the British-made Hawk 108 fighter jet half an hour into the exercise, Affendi said, adding that a panel has been set up to investigate the incident, and the air force will temporarily ground all its Hawk 108 aircraft.
The last mishap involving a Malaysian-owned Hawk fighter jet was a 2003 jet crash off the coast of Kuantan during a training flight, killing both occupants.
Thursday's crash comes six months after an air force twin turboprop Beechcraft B200T crashed at a base in northern Penang state during a training exercise, killing the pilot and injuring three.
In May last year, two air force officers suffered minor injuries when their Aermacchi MB-339CM training jet crashed because of a faulty engine on a training flight, media said.
(Reporting by Joseph Sipalan; Editing by Clarence Fernandez)
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